Math 250B Notes and Videos Videos are at the bottom of the page. You can view the videos on YouTube or stream/download using the link labelled "Download" LECTURE NOTES Sections 11.7, 12.1 and 12.2   Graphing Surfaces Section 12.3   Limits and Continuity Section 12.4   Partial Derivatives Section 12.5   Multivariable Optimization Section 12.6   Linear Approximation Section 12.7   The Multivariable Chain Rule Section 12.8   Direction Derivatives and the Gradient Section 12.9   Lagrange Multipliers Section 12.10   Classifying Critical Points Section 13.1   Double Integration Section 13.2   Setting up Double Integrals Section 13.3   Area and Volume by Double Integration Section 13.4   Double Integration in Polar Coordinates Section 13.5   Applications of Double Integrals Section 13.6   Triple Integrals Section 11.8   Cylindrical and Spherical Coordinates Section 13.7   Integration in Cylindrical and Spherical Coordinates Section 13.8   Surface Area Section 13.9   Change of Variables Section 14.1   Vector Fields Section 14.2   Line Integrals Section 14.3   The Fundamental Theorem and Path Independence Section 14.4   Green's Theorem and 2D Divergence Theorem Section 14.5   Surface Integrals Section 14.6   The 3D Divergence Theorem Section 14.7   Stokes' Theorem VIDEOS 11.7/12.1/12.2 Overview of Multivariable Calculus     VIDEO       Download 11.7/12.1/12.2 Functions of Several Variables     VIDEO       Download 11.7/12.1/12.2 Five Important Surfaces     VIDEO       Download 11.7/12.1/12.2 Graphing Paraboloids     VIDEO       Download 11.7/12.1/12.2 Graphing Spheres     VIDEO       Download 11.7/12.1/12.2 Graphing Cones     VIDEO       Download 11.7/12.1/12.2 Graphing Cylinders     VIDEO       Download 11.7/12.1/12.2 Graphing Planes     VIDEO       Download 12.3 Continuous Multivariable Functions     VIDEO       Download 12.4 Partial Derivatives     VIDEO       Download 12.4 Second-Order Partial Derivatives     VIDEO       Download 12.4 Tangent Planes     VIDEO       Download 12.4 More about Tangent Planes     VIDEO       Download 12.4 Cross Product and Normal Form     VIDEO       Download 12.5 Critical Points     VIDEO       Download 12.5 Absolute Maximum and Minimum     VIDEO       Download 12.5 Absolute Maximum and Minimum: Example     VIDEO       Download 12.6 Differentials     VIDEO       Download 12.6 Linear Approximation     VIDEO       Download 12.6 Absolute Error     VIDEO       Download 12.6 Relative Error     VIDEO       Download 12.7 Multivariable Chain Rule     VIDEO       Download 12.7 Multivariable Chain Rule: Example     VIDEO       Download 12.7 Implicit Partial Differentiation     VIDEO       Download 12.8 The Gradient Vector     VIDEO       Download 12.8 Directional Derivatives     VIDEO       Download 12.8 Maximum Rate of Increase     VIDEO       Download 12.8 Level Curves and Surfaces     VIDEO       Download 12.9 Lagrange Multipliers Part 1     VIDEO       Download 12.9 Lagrange Multipliers Part 2     VIDEO       Download 12.10 Classifying Critical Points     VIDEO       Download 13.1 Double Integration     VIDEO       Download 13.2 The Meaning of Double Integrals     VIDEO       Download 13.2 Vertical and Horizontal Slices     VIDEO       Download 13.2 Swapping Order of Integration     VIDEO       Download 13.3 Area and Volume, Part 1     VIDEO       Download 13.3 Area and Volume, Part 2     VIDEO       Download 13.4 Double Integration in Polar Coordinates     VIDEO       Download 13.4 Polar Area and Volume, Part 1     VIDEO       Download 13.4 Polar Area and Volume, Part 2     VIDEO       Download 13.5 Double Integrals: Mass and Centroid     VIDEO       Download 13.5 Double Integrals: Moment of Inertia     VIDEO       Download 13.6 Volume by Triple Integration, Part 1     VIDEO       Download 13.6 Volume by Triple Integration, Part 2     VIDEO       Download 13.6 Triple Integration: Centroid and Moment of Inertia     VIDEO       Download 11.8 Cylindrical Coordinates     VIDEO       Download 11.8 Spherical Coordinates     VIDEO       Download 13.7 Integration in Cylindrical Coordinates, Part 1     VIDEO       Download 13.7 Integration in Cylindrical Coordinates, Part 2     VIDEO       Download 13.7 Integration in Spherical Coordinates     VIDEO       Download 13.8 Surface Area     VIDEO       Download 13.8 Surface Area of Parametric Surfaces     VIDEO       Download 13.8 Geometry of Surface Area Formulas     VIDEO       Download 13.9 Change of Variables     VIDEO       Download 13.9 Elliptical Change of Variables     VIDEO       Download 13.9 Spherical Correction Factor     VIDEO       Download 14.1 Intro to Vector Fields     VIDEO       Download 14.1 Divergence and Curl     VIDEO       Download 14.2 Line Integrals with respect to Arc Length     VIDEO       Download 14.2 Parametrizing a Curve     VIDEO       Download 14.2 Line Integrals with respect to Coordinates     VIDEO       Download 14.2 Work done by a Force Field     VIDEO       Download 14.3 Conservative Vector Fields     VIDEO       Download 14.3 Fundamental Theorem of Line Integrals     VIDEO       Download 14.3 Path Independence Theorem     VIDEO       Download 14.4 Green's Theorem     VIDEO       Download 14.4 Corollary to Green's Theorem     VIDEO       Download 14.4 2D Flux and 2D Divergence Theorem     VIDEO       Download 14.5 Surface Integrals     VIDEO       Download 14.5 3D Flux, Part 1     VIDEO       Download 14.5 3D Flux, Part 2     VIDEO       Download 14.5 3D Flux, Part 3     VIDEO       Download 14.6 3D Divergence Theorem     VIDEO       Download 14.7 Stokes' Theorem, Part 1     VIDEO       Download 14.7 Stokes' Theorem, Part 2     VIDEO       Download